Viscosity is a characteristic property of common liquids such as water or honey. It is natural to pose the question whether a liquid of electrons in a metal possesses any viscosity at all. A reference point is provided by the Fermi-liquid state of matter, where the static viscosity diverges as 1/T^2. In the opposite case of a quantum critical liquid, AdS/CFT theory predicts a small but finite viscosity, s \hbar / k_B, where s is the entropy density. Viscosity makes the electromagnetic response manifestly non-local, which has important consequences for the interaction with electromagnetic fields. In particular the collective modes of the electron liquid in a metal are significantly different from the model of evanescent electromagnetic waves. One of the most striking and counter-intuitive consequences is, that cooling a clean thin metal film to low temperature has the effect of increasing the amount of mm-wave radiation that leaks through the film. These and other effects of viscosity will be reviewed in this talk.

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